My example of a deep, elegant, and beautiful explanation in science is John Maynard Smith's concept of an evolutionarily stable strategy (ESS). Not only does this wonderfully straightforward idea explain a whole host of biological phenomena, it also provides a very useful heuristic tool to test the plausibility of various types of claims in evolutionary biology, allowing us, for example, to quickly dismiss group-selectionist misconceptions such as the idea that altruistic acts by individuals can be explained by the benefits that accrue to the species as a whole from these acts. Indeed, the idea is so powerful that it explains things which I didn't even realize needed explaining until I was given the explanation! I will now present one such explanation below to illustrate the power of ESS. I should note that while Smith developed ESS using the mathematics of game theory (along with collaborators G. R. Price and G. A. Parker), I will attempt to explain the main idea using almost no math.

So, here is a question: think of common animal species like cats, or dogs, or humans, or golden eagles; why do all of them have (nearly) equal numbers of males and females? Why are there not sometimes 30% males in a species and 70% females? Or the other way? Or some other ratio altogether? Why are sex ratios almost exactly 50/50? I, at least, never even considered the question until I read the incredibly elegant explanation.

Let us consider walruses: they exist in the normal 50/50 sex ratio but most walrus males will die virgins. (But almost all females will mate.) Only a few dominant walrus males monopolize most of the females (in mating terms). So what's the point of having all those extra males around, then? They take up food and resources, but in the only thing that matters to evolution, they are useless, because they do not reproduce. From a species point-of-view, it would be better and more efficient if only a small proportion of walruses were males, and the rest were females, in the sense that such a species of walrus would make much more efficient use of its resources and would, according to the logic of group-selectionists, soon wipe out the actual existing species of walrus with the inefficient 50/50 ratio of males to females. So why don't they?

Here's why: because a population of walruses (of course, you can substitute any of the other animals I have mentioned, including humans, for the walruses in this example) with, say, 10% males and 90% females (or any other non-50/50 ratio) would not be stable over a large number of generations. Why not? Remember that, given the 10% males and 90% females of this example, each male is producing about 9 times as many children as any female (by successfully mating with, on average, close to 9 females). Imagine such a population. If you were a male in this kind of population, it would be to your evolutionary advantage to produce more sons than daughters because each son could be expected to produce roughly 9 times as many offspring as any of your daughters. Let me run through some numbers to make it more clear: suppose that the average male walrus fathers 90 children (only 9 of which will be males and 81 females, on average), and the average female walrus mothers 10 baby walruses (only 1 of which will be a male and 9 will be females). Okay?

Here's the crux of the matter: suppose a mutation arose in one of the male walruses (as it well might over a large number of generations) that made it such that this particular male walrus had more Y (male-producing) sperm than X (female-producing) sperm. In other words, the walrus produced sperm that would result in more male offspring than female ones, this gene would spread like wildfire through the described population. Within a few generations, more and more male walruses would have the gene that makes them have more male offspring than female ones, and soon you would get to the 50/50 ratio that we see in the real world.

The same argument applies for females: any mutation in a female that caused her to produce more male offspring in the population of our example (though sex is determined by the sperm, not the egg, there are other mechanisms the female might employ to affect the sex ratio) than female ones, would spread quickly in this population, changing the ratio from 10/90 closer to 50/50 with each subsequent generation until it actually reaches the 50/50 mark. In fact, any significant deviation from the 50/50 ratio will not be evolutionarily stable for this reason, and will through random mutation soon revert to the 50/50 sex ratio.

One can, of course, use a mirror image of this argument to show that a population of 90% males and 10% females would also soon revert to the 50/50 ratio. So having children with any sex ratio other than 50/50 is not an evolutionarily stable strategy for either males or females. And this is just one example of the explanatory power of ESS.